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If (1 + x +x^2)^n = a0 =a1x + a2x^2 + …....

If `(1 + x +x^2)^n = a_0 =a_1x + a_2x^2 + ….+a_(2n)x^(2n)` then prove that `a_1 +a_3 +a_5 + …..a_(2n - 1) = (3^n - 1)/(2)`

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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 3.1 ( SHORT ANSWER QUESTIONS)
  1. Find the sum of the coefficients of x^(32) and x^(-18) in the expansio...

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  2. If the coefficient of x^11 and x^12 in (2+ (8x)/(3))^n are equal find ...

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  3. If the coefficient of x^10 in (ax^2 + (1)/(bx))^11 is equal to the co...

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  4. Find the numerically greatest terms in the expansion of (2x +3x)^...

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  5. Find the numerically greatest terms in the expansion of (3x-4y)^(14...

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  6. Find the numerically greatest terms in the expansion of (3 + (2x)/(...

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  7. Find the numerically greatest terms in the expansion of (3y + 7x)^10...

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  8. Find the numerically greatest term (s) in the expansion of (4+3x)^(1...

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  9. Find the numerically greatest term (s) in the expansion of (3x+5y)^(...

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  10. Find the numerically greatest term (s) in the expansion of (4a-6b)^(...

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  11. Find the numerically greatest term (s) in the expansion of (3+7x)^(n...

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  12. Find the numerically greatest terms in the expansion of (1 - 5x)^12 w...

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  13. If (1 + x +x^2)^n = a0 +a1x + a2x^2 + ….+a(2n)x^(2n) then prove that ...

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  14. If (1 + x +x^2)^n = a0 +a1x + a2x^2 + ….+a(2n)x^(2n) then prove that ...

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  15. If (1 + x +x^2)^n = a0 =a1x + a2x^2 + ….+a(2n)x^(2n) then prove that ...

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  16. If (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+….+a(2n)x^(2n), then prove tha...

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  17. If (1+x+x^(2)+x^(3))^(7)=b(0)+b(1)x+b^(2)x^(2)+….b(21)x^(21), then fin...

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  18. If (1+x+x^(2)+x^(3))^(7)=b(0)+b(1)x+b^(2)x^(2)+….b(21)x^(21), then fin...

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  19. Find the remainder when 2^(2013) in divided by 17.

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  20. Find the number of irrational terms in the expansion of (5^(1//6)+2^(1...

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